Solve this question please.

Dear Student,
Here is the solution of your asked query:
$$\begin{gathered} \mathrm{Since} \left(\mathrm{x}+\mathrm{k}\right) \mathrm{is} \mathrm{the} \mathrm{GCD} \mathrm{of} \left({\mathrm{x}}^2-2\mathrm{x}-15\right) \mathrm{and} \left({\mathrm{x}}^3+27\right) \\ \mathrm{This} \mathrm{means} \mathrm{x}=-\mathrm{k} \mathrm{is} \mathrm{zero} \mathrm{of} \mathrm{both} \mathrm{given} \mathrm{polynomials}. \\ \mathrm{So} \mathrm{we} \mathrm{have}; \\ {\left(-\mathrm{k}\right)}^2-2\left(-\mathrm{k}\right)-15=0 \\ \Rightarrow {\mathrm{k}}^2+2\mathrm{k}-15=0 \\ \Rightarrow {\mathrm{k}}^2+5\mathrm{k}-3\mathrm{k}-15=0 \\ \Rightarrow \mathrm{k}\left(\mathrm{k}+5\right)-3\left(\mathrm{k}+5\right)=0 \\ \Rightarrow \left(\mathrm{k}-3\right)\left(\mathrm{k}+5\right)=0 \\ \Rightarrow \mathrm{k}=3 \mathrm{and} \mathrm{k}=-5 \end{gathered}$$
Regards